(1) Field of the Invention
The invention relates to an arrangement comprising a non-recursive filter having an input circuit and means coupled to this input circuit for generating a sequence of delayed versions of a signal applied to said input circuit, an output circuit formed by a summing device, a comparator connected to said output circuit, means for applying the filter output signal and a reference signal to said comparator to produce an error signal, and means for weighting said sequence of delayed versions of the input signal in accordance with a sequence of coefficients which are each iteratively adjusted, having variable step-sizes for minimizing a prescribed function of said error signal.
Filters of the above-defined type are known in an analog as well as a digital construction and are, for example used in devices, such as echo cancellers, for "full-duplex" data transmission over two-wire circuits and equalizers for equalizing dispersive channels for data transmission.
Adjusting the filter coefficients can be done in different manners. A method which is used for equalization in particular consists in that the filter coefficients are adjusted in a time interval preceding the actual data transmission, the so-called "training" period, whereafter they are held at the adjusted values during the actual data transmission or are re-adjusted in a wholly adaptive manner, the received data signal being detected and used as the reference signal.
As is known, use can be made of different kinds of algorithms, such as, for example, the "sign" algorithm, the stochastic iteration algorithm and the correlation algorithm, for the control of such filters. For each of these algorithms a choice must be made for the value of the step-size parameter (.alpha.) in each of N control loops by means of which the N filter coefficients can be adjusted. Two factors, namely the adjusting period required and the final error are predominantly decisive for the choice of the value of the step-size parameter (.alpha.). A higher value of the step-size parameter (.alpha.) results in a more rapid convergence and, consequently, a shorter adjusting period, but also results in a greater final error. When the step-size parameter (.alpha.) has a constant value which is not time-variant and which is also the same for all N coefficients, this implies that the choice of the value of the step-size parameter (.alpha.) is based on a compromise. The fact that a relatively long adjusting period of the filter must be tolerated is then often the result of the maximum final error which is still permissible in practice.
The invention results from investigations into the possibility to work with a step-size parameter (.alpha.) whose value can be varied.
(2) Description of the Prior Art
It is assumed that the practical implementation of a non-recursive filter as well as the arrangements in which such a filter is used are sufficiently known from the great number of publications in this field of the art.
Reference is made to reference (D.1), more in particular to FIGS. 1, 2, 3 and 4 thereof and the associated text, as an example of possible analog embodiments of a non-recursive filter used in an adaptive equalizer. A possible digital embodiment of a non-recursive filter used in an adaptive equalizer is disclosed in, for example, reference (D.2).
In the embodiments known from the above-mentioned references (D.1) and (D.2), the step-size parameter (.alpha.) has a constant value which entails, as it must be of small value in order to cause the maximum final error to be small, that the adjusting period is relatively long.
In order to realize an improved convergence and consequently a shorter adjusting period it is already known to use a variable step-size parameter (.alpha.). Reference (D.3), for example, describes an adaptive equalizer provided with a non-recursive filter for a synchronous data transmission system, wherein use is made of two different predetermined step-size parameters .alpha..sub.1 and .alpha..sub.2, wherein .alpha..sub.1 &gt;&gt;.alpha..sub.2 to improve the speed of convergence. Therein the choice of the proper step-size parameter is time-dependent and determined by the beginning and the end of the adjusting period preceding the actual data transmission, the so-called "training" period. Thus, the higher value step-size parameter .alpha..sub.1 is selected at the instant the "training" period starts and the lower value step-size parameter .alpha..sub.2 is selected at the instant the "training" period ends. This strategy has the drawback that at the instant the lower value step-size parameter .alpha..sub.2 is selected, there is as yet no certainty that the error has been reduced to a sufficient extent. This strategy has furthermore the inherent limitation that it can only be used when the actual data transmission is preceded by a "training period".
Another selection criterion disclosed in, for example, reference (D.4) consists in that the higher value step-size parameter .alpha..sub.1 is selected when the amplitude of the error signal exceeds a predetermined fixed reference value, whereas the lower value step-size parameter .alpha..sub.2 is selected when the amplitude of the error signal is below the said reference value. This strategy can indeed be used without the need for a "training" period preceding the actual data transmission but, owing to the use of a fixed reference value, it has the inherent limitation that it can only be used when the level of the signal received in the terminal station varies only a little, because the amplitude of the error signal is also depending on the level of the received signal. As in practice the terminal station must be capable of processing information received over different transmission paths, it is possible that the received signal level varies to a relatively great extent, depending on the transmission path followed. Therefore, this strategy also is not very suitable for use in practice.
It will be clear that the number of possible step-size parameters to be selected need not be restricted to two.
References (D.5) and (D.6) concern themselves with theoretical considerations of the optimum variation of the step-size parameter (.alpha.) as a function of the time and as a function of the N coefficients. However, a simple practical implementation cannot be derived therefrom.